The objective of the research is to develop a mathematical formalism for analyzing plasma wave behavior under complicated geometrical conditions. Emphasis is placed on MHD waves although waves of higher frequency will also be considered. Non-linear interaction of MHD waves can produce a variety of important effects that influence heating, instability, turbulence and transport in plasmas. An example is non-linear Alfven waves which induce current channels via conversion of wave helicity into helicity of the equilibrium magnetic field. This conversion contributes to the plasma current and leads to heating and plasma instability. In addition, circularly polarized Alfven waves can couple to drift waves and evolve into localized vortex structures which give rise to transport within the vortex structures. These will all be explored in some detail with emphasis on laboratory and space plasmas. The areas covered include: 1. Mass flow effects on MHD wave activity 2. MHD processes in the solar corona 3. Transport and injection of Alfven wave helicity 4. Excitation of Alfven vortex structures 5. Phase conjugation via non-linear mixing of plasma waves.
